In a large, heavy pot, heat the oil and butter over medium heat. Brown the chicken pieces, turning them frequently to cook evenly. Reduce the heat to low and add the corn, consomme, and cream. Stir to mix well.

Add the onions, bell pepper, and tomatoes. Season with salt, black pepper, and cayenne. Add the basil and cook over low heat, partially covered, stirring often, until the chicken is tender, 40 minutes to one hour.